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# 1-7.11 work by xiaoyounan

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```									  Hydraulic System
Modeling and Analysis

Guangbin Sun

5/13/2011
1. Modeling Stick-Slip Friction
in valve
• Phenomenon: at low freq., pressure
jump occurs when flow changes
signs; at some freq., oscillation
occurs.
1. Modeling Stick-Slip Friction
in valve
42       F=0.2225hz Mag=100             Torque          40

41

39

40

39                                                      38

38
L_HFE_rtrq

37

37

36                                                      36

35

35

34

33                                                      34

40
0
F=0.4952hz Mag=300
5        10       15        20       25
39
-1      -0.5   0   0.5         1

39                                                    38.5

38                                                     38
L_HFE_rtrq

37                                                    37.5

36                                                     37

35                                                    36.5

34                                                     36
0           5                 10            15           -0.5          0         0.5
1. Modeling Stick-Slip Friction
in valve
Why friction of valve?

Because this phenomena occurs only at low frequency, it should be the
effects of valve friction(especially static friction).
1. Modeling Stick-Slip Friction
in valve
1. Modeling Stick-Slip Friction
in valve
1. Modeling Stick-Slip Friction
in valve
data                                                                                    data

40                                                                                      40
torq(NM)

torq(NM)
35                                                                                      35

30                                                                                      30
0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
time(0.001s)                           4                                                time(0.001s)                           4
x 10                                                                                    x 10
model                                                                                   model

40                                                                                      40
torq(NM)

torq(NM)
35                                                                                      35

30                                                                                      30
0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
time(0.001s)                           4                                                time(0.001s)                           4
x 10                                                                                    x 10

f=0.1hz; mag=100                                                                       f=0.1492hz; mag=100
1. Modeling Stick-Slip Friction
in valve
data                                                                                     data
45                                                                                      45

40                                                                                      40
torq(NM)

torq(NM)
35                                                                                      35

30                                                                                      30
0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2    0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
time(0.001s)                           4                                                 time(0.001s)                           4
x 10                                                                                     x 10
model                                                                                    model
45                                                                                      45

40
torq(NM)

40

torq(NM)
35                                                                                      35

30                                                                                      30
0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2    0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
time(0.001s)                           4
time(0.001s)                           4
x 10                                                                                     x 10

f=0.2225hz; mag=200                                                                     f=0.3319hz; mag=300
1. Modeling Stick-Slip Friction
in valve
data                                                           data
40                                                           42

40
38
torq(NM)

torq(NM)
38
36
36

34                                                           34
0      5000                  10000   15000                   0        5000                  10000   15000
time(0.001s)                                                   time(0.001s)
model                                                          model
40                                                           42

40
38
torq(NM)

torq(NM)
38
36
36

34                                                           34
0      5000                  10000   15000                   0        5000                  10000   15000
time(0.001s)                                                   time(0.001s)

f=0.4592hz; mag=300                                          f=0.7386hz; mag=400
1. Modeling Stick-Slip Friction
in valve
data                                                          data
40                                                          50

40
torq(NM)

torq(NM)
35
30

30                                                          20
0     5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)
model                                                         model
50
45
torq(NM)

torq(NM)
40

40
30

35                                                          20
0     5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)

f=0.7386hz; mag=800                                         f=1.1018hz; mag=800
1. Modeling Stick-Slip Friction
in valve
data                                                           data
60                                                          60
torq(NM)

torq(NM)
40                                                          40

20                                                          20

0     5000                  10000   15000                   0        5000                  10000   15000
time(0.001s)                                                   time(0.001s)
model                                                          model

60                                                          60

torq(NM)
torq(NM)

40                                                          40

20                                                          20

0     5000                  10000   15000                   0        5000                  10000   15000
time(0.001s)                                                   time(0.001s)

f=1.6436hz; mag=800                                         f=2.4517hz; mag=400
2. Modeling Piston Friction
2. Modeling Piston Friction
data                                                      data

40                                                      40
torq(NM)

torq(NM)
35                                                      35

30                                                      30

0     5000                  10000   15000               0       5000                  10000   15000
time(0.001s)                                              time(0.001s)
model                                                     model

40                                                      40
torq(NM)

torq(NM)
35                                                      35

30                                                      30

0     5000                  10000   15000               0       5000                  10000   15000
time(0.001s)                                              time(0.001s)

f=0.1hz; mag=100                                        f=0.1492hz; mag=100
2. Modeling Piston Friction
data                                                          data
45                                                           45

40                                                           40
torq(NM)

torq(NM)
35                                                           35

30                                                           30
0      5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)
model                                                         model
45                                                           45

40                                                           40
torq(NM)

torq(NM)
35                                                           35

30                                                           30
0      5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)

f=0.2225hz; mag=200                                          f=0.3319hz; mag=300
2. Modeling Piston Friction
data                                                         data
40                                                           42

40
38
torq(NM)

torq(NM)
38
36
36

34                                                           34
0      5000                  10000   15000                   0      5000                  10000   15000
time(0.001s)                                                 time(0.001s)
model                                                        model
40                                                           42

40
38
torq(NM)

torq(NM)
38
36
36

34                                                           34
0      5000                  10000   15000                   0      5000                  10000   15000
time(0.001s)                                                 time(0.001s)

f=0.4952hz; mag=300                                          f=0.7386hz; mag=400
2. Modeling Piston Friction
data                                                          data
50
45
torq(NM)

torq(NM)
40
40

35                                                          30

0     5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)
model                                                         model
50
45
torq(NM)

torq(NM)
40
40

35                                                          30

0     5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)

f=0.7386hz; mag=800                                         f=1.1018hz; mag=800
2. Modeling Piston Friction
data                                                          data
60                                                          60
torq(NM)

torq(NM)
40                                                          40

20                                                          20

0     5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)
model                                                         model
60                                                          60
torq(NM)

torq(NM)
40                                                          40

20                                                          20

0     5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)

f=1.6436hz; mag=800                                         f=2.4517hz; mag=400
3. Valve & Piston Friction together
data                                                       data

40                                                          40
torq(NM)

torq(NM)
35                                                          35

30                                                          30

0         5000                  10000   15000               0        5000                  10000   15000
time(0.001s)                                               time(0.001s)
model                                                      model

40                                                          40
torq(NM)

torq(NM)
35                                                          35

30                                                          30

0         5000                  10000   15000               0        5000                  10000   15000
time(0.001s)                                               time(0.001s)

f=0.1hz; mag=100                                         f=0.1492hz; mag=100
3. Valve & Piston Friction together
data                                                          data
45                                                             45

40
torq(NM)

40

torq(NM)
35                                                             35

30                                                             30
0        5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)
model                                                         model
45                                                             45

40                                                             40
torq(NM)

torq(NM)
35                                                             35

30                                                             30
0        5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)

f=0.2225hz; mag=200                                          f=0.3319hz; mag=300
3. Valve & Piston Friction together
data                                                           data
40                                                             42

40
38

torq(NM)
torq(NM)

38
36
36

34                                                             34
0        5000                  10000   15000                   0        5000                  10000   15000
time(0.001s)                                                   time(0.001s)
model                                                          model
40                                                             42

40
38

torq(NM)
torq(NM)

38
36
36

34                                                             34
0        5000                  10000   15000                   0        5000                  10000   15000
time(0.001s)                                                   time(0.001s)

f=0.4952hz; mag=300                                          f=0.7386hz; mag=400
3. Valve & Piston Friction together
data                                                          data
50
45

torq(NM)
torq(NM)

40
40

35                                                            30

0       5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)
model                                                         model
50
45
torq(NM)

torq(NM)
40
40

35                                                            30

0       5000                  10000   15000                   0       5000                  10000   15000
time(0.001s)                                                  time(0.001s)

f=0.7386hz; mag=800                                         f=1.1018hz; mag=800
3. Valve & Piston Friction together
data                                                        data

60                                                           60

torq(NM)
torq(NM)

40                                                           40

20                                                           20

0      5000                  10000   15000                   0     5000                  10000   15000
time(0.001s)                                                time(0.001s)
model                                                       model

60                                                           60

torq(NM)
torq(NM)

40                                                           40

20                                                           20

0      5000                  10000   15000                   0     5000                  10000   15000
time(0.001s)                                                time(0.001s)

f=1.6436hz; mag=800                                        f=2.4517hz; mag=400
4. Moment Arm
Moment Arm
0.044
Mine
Previous
0.042

0.04
X dot/ th dot

0.038

0.036

0.034

0.032
-1   -0.5   0       0.5        1   1.5              2

There’re 2 parameters in previous version
(hfe.m) which I think are wrong.
L5=0.27(should be 0.2748); th5=th4-
80*pi/180(should be 75.5);
4. Moment Arm
5. Simulate Complex Model
•Complex Model--Physics-based Model

                                     
Assume x1   ; x 2   ; x 3  p1 ; x 4  p2 ; x 5  xv ; x 6  xv ;

x1  x2
     L                             mgl sin( x1 )
x2       [( x3   x4 ) Ap  F f ] 
Ja                                 Ja
   E1' ( x3 )
x3             [Q1 ( x3 , x5 )  Ap c1 x2  K Li ( x4  x3 )]
V1 ( x1 )
    '
E2 ( x4 )
x4            [Q2 ( x4 , x5 )   Ap c1 x2  K Li ( x4  x3 )]
V2 ( x1 )

x5  x6

x6  2n x6  n x5  Ku (approximated )
2

x2
where, Ff   x2  sign( x2 )[ Fc 0  Fs 0 exp(              )]
cs
5. Simulate Complex Model
5. Simulate Complex Model
Values of Coefficients
names    description         values        units
Ps       Supply pressure     20684271.87   Pa
PT       Return pressure     Ps/20         Pa
zeta     Damping             0.5           ___
coefficient of
valve
wn       Natural frequency   200*2*pi      rad/s
of valve
Vpl      Oil volume in      1.7093e-005    m^3
pipelines between
valve and cylinder
K        Valve gain          0.0381        ___
m        Mass of load        12.7002       kg
l        Length of CoM       0.5181        m
from pivot
Ap       Piston area         1.9793e-004   m^2
alpha    Piston area ratio   0.635         ___
5. Simulate Complex Model
Values of Coefficients
names          description         values        units
Param for viscous 3200
friction
Param for           unused
coulomb friction
Param for static    unused
friction
Param for static    unused
friction(Stribeck
velocity)
Flow coefficient of 1.4982e-6
valve
KLi    Internal leakage    1.0390e-013
coefficient
Moment Arm          changing      m
L      Actuator length     changing      m
Emax       Maximum bulk        1.3410e+009   Pa
5. Simulate Complex Model
(Last Work) Around
different angles
4
Commanded valve -> Torq                                                      Commanded valve -> Torq
10                                                                          100
x1=-0.5                                                                  x1=-0.5
x1=0                                                                     x1=0
x1=0.5                                                                   x1=0.5
x1=1                              50
x1=1
x1=1.5                                                                   x1=1.5
3
10

Phase (degrees)
Log Magnitude

0

-50
2
10

-100

1
10                                                                          -150
-1    0                        1                  2                          -1    0                        1              2
10     10                   10                     10                        10     10                   10                 10
Log Frequency                                                                Log Frequency
5. Simulate Complex Model— no gravity (V
changing with angles)
Commanded valve -> Torq
3                                                                                              Commanded valve -> Torq
10
100
x1=-0.5                                                                      x1=-0.5
x1=0                                                                         x1=0
x1=0.5                                                                       x1=0.5
x1=1                                  50
x1=1
x1=1.5                                                                       x1=1.5
2
10

Phase (degrees)
Log Magnitude

0

-50
1
10

-100

0                                                                                    -150
10                                                                                          -1     0                       1              2
-1             0                       1                2                            10     10                   10
Commanded valve -> Vel                 10
10
1
10
10 Commanded valve -> vel                 10
10                                                                                      50           Log Frequency
Log Frequency
x1=-0.5                                                                      x1=-0.5
x1=0                                                                         x1=0
x1=0.5                                  0                                    x1=0.5
0                                            x1=1                                                                         x1=1
10                                                                                                                             x1=1.5
x1=1.5
-50
Phase (degrees)
Log Magnitude

-1                                                                                -100
10

-150

-2
10
-200

-3                                                                                -250
-1     0                       1              2
10                                                                                        10     10                    10                10
-1        0                         1                  2
10           10                     10                 10                                         Log Frequency
5. Simulate Complex Model-- no gravity (V
changing with angles)
Commanded valve -> pos
0                                                                                   Commanded valve -> pos
10
-50
x1=-0.5
x1=-0.5
x1=0
x1=0
x1=0.5                           -100                                    x1=0.5
x1=1                                                                     x1=1
x1=1.5                                                                   x1=1.5
-150

Phase (degrees)
Log Magnitude

-1
10                                                                        -200

-250

-300

-2
10                                                                        -350
-1                    0                       1                          -1    0                        1              2
10                   10                       10                        10     10                   10                 10
Log Frequency                                                        Log Frequency
5. Simulate Complex Model—with
gravity(V=constant)
3
Commanded valve -> Torq                                                  Commanded valve -> Torq
10                                                                      100
x1=-0.5                                                                  x1=-0.5
x1=0                                                                     x1=0
x1=0.5                                                                   x1=0.5
50
x1=1                                                                     x1=1
x1=1.5                                                                   x1=1.5
2
10

Phase (degrees)
Log Magnitude

0

-50
1
10

-100

0
10                                                                      -150
-1    0                        1              2                          -1    0                        1              2
10     10                   10                 10                        10     10                   10                 10
Log Frequency                                                            Log Frequency
5. Simulate Complex Model—moment arm
10
3                   changing with angles
Commanded valve -> Torq
150
Commanded valve -> Torq

x1=-0.5
x1=-0.5
x1=0                                                                         x1=0
x1=0.5                           100                                         x1=0.5
x1=1                                                                         x1=1
x1=1.5                                                                       x1=1.5
2
10                                                                                50

Phase (degrees)
Log Magnitude

0

1
10                                                                                -50

-100

0
10                                                                               -150
-1             0                        1              2                          -1    0                        1                  2
10              10                    10                10                        10     10                      10                  10
Log Frequency                                                               Log Frequency
Commanded valve -> vel                                                       Commanded valve -> Vel
2                                                                               150
10
x1=-0.5                                                                       x1=-0.5
x1=0                             100                                          x1=0
1
10                                              x1=0.5                                                                        x1=0.5
x1=1                                                                          x1=1
50
x1=1.5                                                                        x1=1.5
0
10
0
Phase (degrees)
Log Magnitude

-1
10                                                                                -50

-2                                                                              -100
10

-150
-3
10
-200

-4
10                                                                               -250
-1        0                        1              2
10           10                    10                10                          -1        0                        1                  2
10     10                       10                  10
Log Frequency
5. Simulate Complex Model—Different bulk
modulus(last work)

4
Commanded valve -> Torq                                                       Commanded valve -> Torq
10                                                                             100
Emax=1.341e9                                                                  Emax=1.341e9
0.5Emax                                                                       0.5Emax
2Emax                                                                         2Emax
50

3
10

Phase (degrees)
Log Magnitude

0

-50
2
10

-100

1
10                                                                             -150
-1      0                        1                   2                          -1    0                        1                   2
10       10                   10                      10                        10     10                   10                      10
Log Frequency                                                                 Log Frequency
5. Simulate Complex Model—Different bulk
modulus(last work)

2
Commanded valve -> Angle position                                                   Commanded valve -> Angle position
10                                                                                     -50
Emax=1.341e9                                                                        Emax=1.341e9
0.5Emax                                                                             0.5Emax
1                                                                                    -100
10                                              2Emax                                                                               2Emax

-150
0
10

Phase (degrees)
Log Magnitude

-200
-1
10
-250
-2
10
-300

-3
10                                                                                    -350

-4
10                                                                                    -400
-1         0                      1                       2                          -1        0                      1                       2
10        10                     10                       10                        10        10                     10                       10
Log Frequency                                                                       Log Frequency
5. Simulate Complex Model—Different length between
CoG and hip pivot(last work)

4
Commanded valve -> Torq                                                           Commanded valve -> Torq
10                                                                               100
CoG2Pivot=0.5181                                                                  CoG2Pivot=0.5181
0.5CoG2Pivot                                                                      0.5CoG2Pivot
2CoG2Pivot                                                                        2CoG2Pivot
50

3
10

Phase (degrees)
Log Magnitude

0

-50
2
10

-100

1
10                                                                               -150
-1    0                        1                       2                          -1    0                        1                       2
10     10                   10                          10                        10     10                   10                          10
Log Frequency                                                                     Log Frequency
5. Simulate Complex Model—Different length between
CoG and hip pivot(last work)

2
Commanded valve -> Angle position                                                   Commanded valve -> Angle position
10                                                                                      0
CoG2Pivot=0.5181                                                                    CoG2Pivot=0.5181
0.5CoG2Pivot                               -50                                      0.5CoG2Pivot
1
10                                         2CoG2Pivot                                                                          2CoG2Pivot

-100
0
10
-150

Phase (degrees)
Log Magnitude

-1
10                                                                                   -200

-2
-250
10

-300
-3
10
-350

-4
10                                                                                   -400
-1        0                      1                       2                          -1        0                      1                       2
10       10                     10                       10                        10        10                     10                       10
Log Frequency                                                                       Log Frequency
conclusion
• Valve and piston frictions together are responsible for the load
oscillation or jump behavior at low frequency.
• Moment Arm:
• Within the range of 0 to 1 radian, moment arm approximates
0.0375m with good accuracy.
• System Features of Frequency Response:
• 1. Moment arm and gravity effects are most important,
• 2. Piston and ring volume have less effects for our case,
• 3. Bulk modulus has great effects (conclusion of last work),
• 4. Mass distribution affects dynamics intensively (conclusion of last
work).
• 5. The dynamics of the system is position-dependent and varies
obviously when angle limit is approached.
What next?
• Simulate in
Matlab/simMechanics,simHydraulics
• The Final Model?
• Turn to control?
Thank you

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